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Telekinesis Axon

Telekinesis Axon is a camera calibration library for the Telekinesis ecosystem, with a C++ core (targets, calibration, geometry, quality) exposed to Python via pybind11. It supports intrinsic calibration, eye-in-hand (hand-eye) extrinsic calibration, multi-camera extrinsic calibration, and benchmarking, built on OpenCV.

The hardware-driving runtime layer (DataCollector, PerturbationSampler) stays pure Python — camera/robot SDKs are inherently async/IO-bound and don't benefit from a native rewrite.

Installation

pip install telekinesis-axon

Ships as a prebuilt wheel (Linux/Windows, Python 3.11/3.12) from Telekinesis's private package registry — no C++ toolchain needed. If you're building from source instead (e.g. contributing to axon itself), see DEVELOPMENT.md.

Targets

Define your calibration board once and pass it to any calibrator:

from telekinesis.axon.targets import ChessboardTarget, CharucoTarget, ArucoTarget

chessboard = ChessboardTarget(size=(9, 6), square_size=0.025)  # meters

charuco = CharucoTarget(
    squares_x=6,
    squares_y=9,
    square_length=0.012,
    marker_length=0.009,
    aruco_dict_id="DICT_4X4_1000",  # or the raw cv2.aruco.DICT_4X4_1000 int
)

aruco = ArucoTarget(
    board_size=(5, 7),
    marker_length=0.025,
    marker_separation=0.005,
)

Intrinsic Calibration

A single IntrinsicCalibrator dispatches on the target type you pass it — no more separate ArucoIntrinsicCalibrator / CharucoIntrinsicCalibrator subclasses or an IntrinsicBackend indirection:

from telekinesis.axon import IntrinsicCalibrator, IntrinsicOptions
from telekinesis.axon.targets import CharucoTarget

target = CharucoTarget(squares_x=6, squares_y=9, square_length=0.012, marker_length=0.009)

options = IntrinsicOptions()
options.per_view_error_threshold = 0.8

calibrator = IntrinsicCalibrator(target, options)
result = calibrator.calibrate(images)

result.ok  # bool
result.intrinsic_matrix  # (3, 3) np.ndarray
result.distortion_coefficients
result.reprojection_error
result.successful_indices
result.low_view_error_indices

Eye-in-Hand Calibration

Calibrate the transform between the camera and the robot TCP. Requires images of a calibration board alongside the robot's TCP pose (robot_T_tcp as 4×4 homogeneous matrices) for each frame.

from telekinesis.axon import EyeInHandCalibrator
from telekinesis.axon.targets import CharucoTarget

target = CharucoTarget(squares_x=6, squares_y=9, square_length=0.012, marker_length=0.009)

calibrator = EyeInHandCalibrator(target)

result = calibrator.calibrate(
    robot_T_tcp_list=robot_poses,  # list of (4, 4) np.ndarray
    image_list=images,
    method="TSAI",
)

result.ok  # bool
result.tcp_T_camera  # (4, 4) np.ndarray
result.intrinsic_matrix
result.distortion_coefficients
result.reprojection_error
result.consistency  # TargetConsistencyStats, when result.has_consistency

Pass pre-computed per-frame poses

If you have camera_T_target transforms from an external source, pass them via camera_T_target_list to skip EyeInHandCalibrator's internal solvePnP. The caller is responsible for aligning robot_T_tcp_list and image_list to it.

result = calibrator.calibrate(
    robot_T_tcp_list=robot_poses,
    image_list=images,
    camera_T_target_list=external_camera_T_target_list,
    intrinsic_matrix=K,
    distortion_coefficients=d,
)

Multi-Camera Calibration

Calibrate N ≥ 2 synchronized cameras against a reference camera via pairwise cv::stereoCalibrate, with an automatic triangulation validation pass:

from telekinesis.axon import MultiCameraCalibrator
from telekinesis.axon.targets import CharucoTarget

target = CharucoTarget(squares_x=6, squares_y=9, square_length=0.012, marker_length=0.009)

calibrator = MultiCameraCalibrator(target, num_cameras=3, reference_index=1)
result = calibrator.calibrate(image_lists)  # image_lists[cam][frame]

result.ok  # True iff every non-reference pair solved
result.reference_T_camera_list  # per-camera (4, 4) np.ndarray
result.intrinsic_matrices
result.pair_reprojection_errors

Benchmarking

Cross-validate a target/IntrinsicOptions configuration and, optionally, a hand-eye round trip:

from telekinesis.axon import CalibrationBenchmark, IntrinsicOptions
from telekinesis.axon.targets import CharucoTarget

target = CharucoTarget(squares_x=6, squares_y=9, square_length=0.012, marker_length=0.009)

bench = CalibrationBenchmark()
result = bench.run(
    images=my_images,
    target=target,
    options=IntrinsicOptions(),
    robot_poses=my_robot_poses,  # optional — enables the round-trip metric
    eye_in_hand_options=IntrinsicOptions(),  # optional
    n_splits=5,
)
CalibrationBenchmark.save_json([result], "calibration_benchmark.json")
print(CalibrationBenchmark.format_results([result]))

Output (calibration_benchmark.json):

{
  "run_timestamp": "2026-05-18T...",
  "results": [
    {
      "backend_name": "OpenCV",
      "reprojection_error": 0.42,
      "held_out_reprojection_error": 0.61,
      "hand_eye_roundtrip_error": 1.3,
      "camera_matrix": [[fx, 0, cx], [0, fy, cy], [0, 0, 1]],
      "dist_coeffs": [...]
    }
  ]
}

Resources

• Examples — Telekinesis Examples
• Documentation — Telekinesis Documentation

Support

• Open an issue on GitHub
• Contact the team at support@telekinesis.ai or on Discord

License

Proprietary — © Telekinesis. All rights reserved.